The NSW BDM has 19 May 1866 for that marriage. I can see that the Military record has the Rev as John REID. Likely that would be Rev John REID of the Scots Church, Sydney. So likely a Presbyterian marriage, and probably at the Scots Church which stood in Sydney CBD until it was demolished in the 1920s to make way for the Sydney Harbour Bridge.
My transcription of the Military record which is all in the one hand, likely the Adjutant:
15th Brigade of the Royal Regiment of Artillery
Registry of Marriages, page 16, entry 2.
Corporal John George PICKERING, Bachelor,
Annie BUTLER, Spinster,
married 19 May 1866, by Rev John REID
R Pickering and Taylor Emma, witnesses
May I mention that it is possible that there is scant further information to be found on the civil registration of that marriage. The Presbyterian Church was one of the many denominations that were in a very long dispute with the secular administrative bods at the Registrar Generals Office, and for about four decades only summary information was submitted by the clergy to the BDM. The clergy usually recorded the full information required by the relevant NSW BDM Marriage Acts, but hesitated in providing all that depth of detail to the civil authorities. Civil registration commenced in NSW in 1856. The dispute was not resolved until the mid 1890s. So, please do NOT waste your pennies on ordering the 'real deal' certificate from the NSW BDM - but ... the best 'work around' is usually to order an official transcription from one of the official transcription agents. They often have 'specials' at this time of the year, so for about $20 Au or less you could get all the info that is on the actual real deal certificate, but without the fancy watermark certification.
https://www.rootschat.com/forum/index.php/topic,300394.0.htmlJM